How to Mathematically Choose the Optimal Bins for Your Histogram

Choosing the optimal number of bins for a histogram can be addressed using a rigorous Bayesian approach. This method treats each potential bin configuration as a separate model and uses information theory to balance accuracy against complexity. Instead of selecting a single best configuration, the approach creates a weighted average of all considered models to produce a more robust density estimate. The technique can be further extended to accommodate unequal bin sizes and to visualize the uncertainty of the density estimate with error bars.